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Fractal Profit Landscape of the Stock Market
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2012 (English)In: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 7, no 4, e33960- p.Article in journal (Refereed) Published
Abstract [en]

We investigate the structure of the profit landscape obtained from the most basic, fluctuation based, trading strategy applied for the daily stock price data. The strategy is parameterized by only two variables, p and q Stocks are sold and bought if the log return is bigger than p and less than -q, respectively. Repetition of this simple strategy for a long time gives the profit defined in the underlying two-dimensional parameter space of p and q. It is revealed that the local maxima in the profit landscape are spread in the form of a fractal structure. The fractal structure implies that successful strategies are not localized to any region of the profit landscape and are neither spaced evenly throughout the profit landscape, which makes the optimization notoriously hard and hypersensitive for partial or limited information. The concrete implication of this property is demonstrated by showing that optimization of one stock for future values or other stocks renders worse profit than a strategy that ignores fluctuations, i.e., a long-term buy-and-hold strategy.

Place, publisher, year, edition, pages
2012. Vol. 7, no 4, e33960- p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-177631DOI: 10.1371/journal.pone.0033960ISI: 000305336000007OAI: oai:DiVA.org:uu-177631DiVA: diva2:541399
Available from: 2012-07-17 Created: 2012-07-17 Last updated: 2017-12-07Bibliographically approved

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